We study two galaxy clusters with radio relics, 1RXS J0603.3+4214 and RXC J1053.7+5453, through X-ray and radio observations. Radio relics are diffuse non-thermal radio sources found in outskirts of galaxy clusters. Because of their shape and location, they are thought to be related to cluster merger shocks. The galaxy cluster 1RXS J0603.3+4214 has a well-known linear-shape “toothbrush” radio relic. We investigate the temperature structure across the relic to constrain the Mach number of the associated shock. The results are compared with radio spectral results, which suggest that a simple diffusive shock acceleration model does not hold for this relic. The RXC J1053.7+5453 harbors a standard arc-like relic. We also get the Mach number from the temperature profile. In addition, we found an edge-like structure in the X-ray image between the X-ray peak and relic. We investigate the density and temperature profiles across the edge and found that the structure is likely relevant to not a shock but a contact discontinuity.
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